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An improved feed-forward carrier phase estimation scheme with further complexity reduction is presented and numerically verified for quadrature amplitude modulation (QAM) formats. Based on the blind phase search (BPS) algorithm, a general two-stage configuration is first derived by removing several restrictions assumed in the prior art. Two guidelines for determining the design parameters are then proposed to minimize the computational complexity while mitigating the pattern effect and maintaining the tolerance to laser linewidth. Taking square 64QAM as an example, the computational efforts can be reduced by a factor of 4 while keeping the same tolerance to laser linewidth as compared to a single-stage BPS estimator.